Subgroups — C₁₃₉×#35666 #48030262

Order 35584.

4918 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×2₋¹⁺⁴×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#536×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	C₂²×C₄⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2434×C₁₃₉	C₂	1	8	yes	maximal, complemented
5	#2432×C₁₃₉	C₂	1	8	yes	maximal, complemented
6	#2406×C₁₃₉	C₂	1	8	yes	maximal, complemented
7	#2310×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2297×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	C₂×2₋¹⁺⁴×C₁₃₉	—	2	16	no	—
10	C₂×2₋¹⁺⁴×C₁₃₉	—	2	8	no	—
11	C₂²×#41×C₁₃₉	C₂²	1	4	yes	—
12	C₂²×#41×C₁₃₉	C₂²	1	4	yes	—
13	C₂²×#41×C₁₃₉	C₂²	1	2	yes	—
14	C₂³×Q₈×C₁₃₉	C₂²	1	4	yes	—
15	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
16	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
17	#536×C₁₃₉	—	2	16	no	—
18	C₂×C₄⋊Q₈×C₁₃₉	—	2	8	no	—
19	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	8	yes	—
20	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
21	C₂×#124×C₁₃₉	C₂²	1	4	yes	—
22	C₂×#123×C₁₃₉	C₂²	1	8	yes	—
23	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	8	yes	—
24	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
25	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
26	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
27	#395×C₁₃₉	C₂²	1	16	yes	—
28	#394×C₁₃₉	C₂²	1	16	yes	—
29	#391×C₁₃₉	C₂²	1	4	yes	—
30	#391×C₁₃₉	C₂²	1	8	yes	—
31	#390×C₁₃₉	C₂²	1	4	yes	—
32	#386×C₁₃₉	C₂²	1	8	yes	—
33	#385×C₁₃₉	C₂²	1	32	yes	—
34	#381×C₁₃₉	C₂²	1	4	yes	—
35	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	8	yes	—
36	2₋¹⁺⁴×C₁₃₉	—	2	128	no	—
37	C₂×#41×C₁₃₉	—	2	16	no	—
38	C₂×#41×C₁₃₉	—	2	32	no	—
39	C₂×#41×C₁₃₉	—	2	16	no	—
40	C₂×#41×C₁₃₉	—	2	16	no	—
41	C₂×#41×C₁₃₉	—	2	16	no	—
42	C₂×#41×C₁₃₉	—	2	8	no	—
43	C₂×#41×C₁₃₉	—	2	8	no	—
44	C₂×#41×C₁₃₉	D₄	1	16	yes	—
45	C₂²×Q₈×C₁₃₉	—	2	16	no	—
46	C₂²×Q₈×C₁₃₉	—	2	16	no	—
47	C₂²×Q₈×C₁₃₉	—	2	16	no	—
48	C₂²×Q₈×C₁₃₉	—	2	8	no	—
49	C₂²×Q₈×C₁₃₉	—	2	4	no	—
50	C₂²×Q₈×C₁₃₉	—	2	8	no	—
51	C₂²×Q₈×C₁₃₉	D₄	1	8	yes	—
52	C₂²×Q₈×C₁₃₉	C₂³	1	4	yes	—
53	C₂²×Q₈×C₁₃₉	C₂³	1	4	yes	—
54	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
55	C₂²×Q₈×C₁₃₉	C₂³	1	4	yes	—
56	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
57	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
58	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
59	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
60	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
61	C₂³×C₄×C₁₃₉	C₂³	1	8	yes	—
62	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
63	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
64	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
65	C₄⋊Q₈×C₁₃₉	—	2	32	no	—
66	C₄⋊Q₈×C₁₃₉	—	2	16	no	—
67	#124×C₁₃₉	—	2	16	no	—
68	#123×C₁₃₉	—	2	32	no	—
69	C₂²⋊Q₈×C₁₃₉	—	2	32	no	—
70	#117×C₁₃₉	—	2	8	no	—
71	C₂×C₄⋊C₄×C₁₃₉	—	2	16	no	—
72	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	16	yes	—
73	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	16	yes	—
74	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
75	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
76	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	16	yes	—
77	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	16	yes	—
78	C₂×C₄²×C₁₃₉	—	2	4	no	—
79	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
80	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
81	#95×C₁₃₉	C₂³	1	16	yes	—
82	#95×C₁₃₉	C₂³	1	16	yes	—
83	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
84	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
85	#41×C₁₃₉	—	2	128	no	—
86	#41×C₁₃₉	—	2	128	no	—
87	#41×C₁₃₉	—	2	64	no	—
88	C₂×Q₈×C₁₃₉	—	2	128	no	—
89	C₂×Q₈×C₁₃₉	—	2	32	no	—
90	C₂×Q₈×C₁₃₉	—	2	8	no	—
91	C₂×Q₈×C₁₃₉	—	2	16	no	—
92	C₂×Q₈×C₁₃₉	—	2	4	no	—
93	C₂×Q₈×C₁₃₉	—	2	8	no	—
94	C₂×Q₈×C₁₃₉	—	2	4	no	—
95	C₂×Q₈×C₁₃₉	—	2	8	no	—
96	C₂×Q₈×C₁₃₉	—	2	8	no	—
97	C₂×Q₈×C₁₃₉	—	2	8	no	—
98	C₂×Q₈×C₁₃₉	—	2	8	no	—
99	C₂×Q₈×C₁₃₉	—	4	16	no	—
100	C₂×Q₈×C₁₃₉	C₂×D₄	1	8	yes	—
101	C₂×Q₈×C₁₃₉	C₂×D₄	1	16	yes	—
102	C₂×D₄×C₁₃₉	—	2	16	no	—
103	C₂×D₄×C₁₃₉	—	2	8	no	—
104	C₂×D₄×C₁₃₉	—	2	8	no	—
105	C₂×D₄×C₁₃₉	—	2	8	no	—
106	C₂×D₄×C₁₃₉	—	2	4	no	—
107	C₂×D₄×C₁₃₉	—	2	4	no	—
108	C₂×D₄×C₁₃₉	C₂×D₄	1	16	yes	—
109	C₂×D₄×C₁₃₉	C₂×D₄	1	8	yes	—
110	C₂²×C₄×C₁₃₉	—	2	4	no	—
111	C₂²×C₄×C₁₃₉	—	2	16	no	—
112	C₂²×C₄×C₁₃₉	—	2	8	no	—
113	C₂²×C₄×C₁₃₉	—	2	16	no	—
114	C₂²×C₄×C₁₃₉	—	2	16	no	—
115	C₂²×C₄×C₁₃₉	—	2	8	no	—
116	C₂²×C₄×C₁₃₉	—	2	8	no	—
117	C₂²×C₄×C₁₃₉	—	2	8	no	—
118	C₂²×C₄×C₁₃₉	—	2	4	no	—
119	C₂²×C₄×C₁₃₉	—	2	8	no	—
120	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
121	C₂²×C₄×C₁₃₉	C₂×D₄	1	16	yes	—
122	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
123	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
124	C₂²×C₄×C₁₃₉	C₂⁴	1	8	yes	—
125	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
126	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
127	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
128	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
129	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
130	C₄⋊C₄×C₁₃₉	—	2	32	no	—
131	C₄⋊C₄×C₁₃₉	—	2	8	no	—
132	C₄⋊C₄×C₁₃₉	—	2	32	no	—
133	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
134	C₂²⋊C₄×C₁₃₉	—	2	32	no	—
135	C₂²⋊C₄×C₁₃₉	—	2	32	no	—
136	C₄²×C₁₃₉	—	2	8	no	—
137	C₄²×C₁₃₉	—	2	8	no	—
138	C₂³×C₁₃₉	—	2	4	no	—
139	C₂³×C₁₃₉	—	2	4	no	—
140	C₂³×C₁₃₉	—	2	4	no	—
141	C₂³×C₁₃₉	—	2	16	no	—
142	C₂³×C₁₃₉	C₂²×D₄	1	8	yes	—
143	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
144	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
145	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
146	Q₈×C₁₃₉	—	2	32	no	—
147	Q₈×C₁₃₉	—	2	16	no	—
148	Q₈×C₁₃₉	—	2	32	no	—
149	Q₈×C₁₃₉	—	4	16	no	—
150	D₄×C₁₃₉	—	2	32	no	—
151	D₄×C₁₃₉	—	2	32	no	—
152	D₄×C₁₃₉	—	2	16	no	—
153	C₂×C₄×C₁₃₉	—	2	16	no	—
154	C₂×C₄×C₁₃₉	—	2	64	no	—
155	C₂×C₄×C₁₃₉	—	2	16	no	—
156	C₂×C₄×C₁₃₉	—	2	4	no	—
157	C₂×C₄×C₁₃₉	—	2	4	no	—
158	C₂×C₄×C₁₃₉	—	2	8	no	—
159	C₂×C₄×C₁₃₉	—	2	4	no	—
160	C₂×C₄×C₁₃₉	—	2	4	no	—
161	C₂×C₄×C₁₃₉	—	2	32	no	—
162	C₂×C₄×C₁₃₉	—	2	8	no	—
163	C₂×C₄×C₁₃₉	—	2	8	no	—
164	C₂×C₄×C₁₃₉	—	2	4	no	—
165	C₂×C₄×C₁₃₉	—	2	16	no	—
166	C₂×C₄×C₁₃₉	—	4	8	no	—
167	C₂×C₄×C₁₃₉	#120	1	16	yes	—
168	C₂×C₄×C₁₃₉	C₂²×D₄	1	8	yes	—
169	C₂×C₄×C₁₃₉	C₂²×D₄	1	8	yes	—
170	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
171	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
172	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
173	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	8	yes	complemented
174	C₂²×C₁₃₉	—	2	4	no	—
175	C₂²×C₁₃₉	—	2	8	no	—
176	C₂²×C₁₃₉	—	2	8	no	—
177	C₂²×C₁₃₉	—	2	16	no	—
178	C₂²×C₁₃₉	—	4	8	no	—
179	C₂²×C₁₃₉	—	4	8	no	—
180	C₂²×C₁₃₉	C₂×#120	1	4	yes	—
181	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
182	C₂²×C₁₃₉	C₂³×D₄	1	2	yes	—
183	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	4	yes	—
184	C₄×C₁₃₉	—	2	8	no	—
185	C₄×C₁₃₉	—	2	8	no	—
186	C₄×C₁₃₉	—	2	8	no	—
187	C₄×C₁₃₉	—	4	4	no	—
188	C₄×C₁₃₉	—	4	8	no	—
189	C₄×C₁₃₉	C₂×#120	1	8	yes	—
190	C₂×C₁₃₉	—	2	4	no	—
191	C₂×C₁₃₉	—	4	8	no	—
192	C₂×C₁₃₉	C₂²×#120	1	1	yes	characteristic
193	C₂×C₁₃₉	#3486	1	2	yes	—
194	C₂×C₁₃₉	#3499	1	4	yes	—
195	#35666	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
196	C₁₃₉	#35666	1	1	yes	characteristic, direct product factor, Sylow
197	C₂²×2₋¹⁺⁴	C₂×C₁₃₉	1	1	yes	characteristic
198	C₂×#536	C₂×C₁₃₉	1	2	yes	complemented
199	C₂²×C₄⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
200	#2434	C₂×C₁₃₉	1	8	yes	complemented
201	#2432	C₂×C₁₃₉	1	8	yes	complemented
202	#2406	C₂×C₁₃₉	1	8	yes	complemented
203	#2310	C₂×C₁₃₉	1	1	yes	characteristic, complemented
204	#2297	C₂×C₁₃₉	1	2	yes	complemented
205	C₂×2₋¹⁺⁴	—	2	16	no	—
206	C₂×2₋¹⁺⁴	—	2	8	no	—
207	C₂²×#41	C₂²×C₁₃₉	1	4	yes	—
208	C₂²×#41	C₂²×C₁₃₉	1	4	yes	—
209	C₂²×#41	C₂²×C₁₃₉	1	2	yes	—
210	C₂³×Q₈	C₂²×C₁₃₉	1	4	yes	—
211	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
212	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
213	#536	—	2	16	no	—
214	C₂×C₄⋊Q₈	—	2	8	no	—
215	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	8	yes	—
216	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
217	C₂×#124	C₂²×C₁₃₉	1	4	yes	—
218	C₂×#123	C₂²×C₁₃₉	1	8	yes	—
219	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	8	yes	—
220	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
221	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
222	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
223	#395	C₂²×C₁₃₉	1	16	yes	—
224	#394	C₂²×C₁₃₉	1	16	yes	—
225	#391	C₂²×C₁₃₉	1	8	yes	—
226	#391	C₂²×C₁₃₉	1	4	yes	—
227	#390	C₂²×C₁₃₉	1	4	yes	—
228	#386	C₂²×C₁₃₉	1	8	yes	—
229	#385	C₂²×C₁₃₉	1	32	yes	—
230	#381	C₂²×C₁₃₉	1	4	yes	—
231	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	8	yes	—
232	2₋¹⁺⁴	—	2	128	no	—
233	C₂×#41	—	2	16	no	—
234	C₂×#41	—	2	32	no	—
235	C₂×#41	—	2	16	no	—
236	C₂×#41	—	2	16	no	—
237	C₂×#41	—	2	16	no	—
238	C₂×#41	—	2	8	no	—
239	C₂×#41	—	2	8	no	—
240	C₂×#41	D₄×C₁₃₉	1	16	yes	—
241	C₂²×Q₈	—	2	16	no	—
242	C₂²×Q₈	—	2	16	no	—
243	C₂²×Q₈	—	2	16	no	—
244	C₂²×Q₈	—	2	8	no	—
245	C₂²×Q₈	—	2	4	no	—
246	C₂²×Q₈	—	2	8	no	—
247	C₂²×Q₈	D₄×C₁₃₉	1	8	yes	—
248	C₂²×Q₈	C₂³×C₁₃₉	1	4	yes	—
249	C₂²×Q₈	C₂³×C₁₃₉	1	4	yes	—
250	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
251	C₂²×Q₈	C₂³×C₁₃₉	1	4	yes	—
252	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
253	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
254	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
255	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
256	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
257	C₂³×C₄	C₂³×C₁₃₉	1	8	yes	—
258	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
259	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
260	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
261	C₄⋊Q₈	—	2	32	no	—
262	C₄⋊Q₈	—	2	16	no	—
263	#124	—	2	16	no	—
264	#123	—	2	32	no	—
265	C₂²⋊Q₈	—	2	32	no	—
266	#117	—	2	8	no	—
267	C₂×C₄⋊C₄	—	2	16	no	—
268	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	16	yes	—
269	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
270	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	16	yes	—
271	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
272	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	16	yes	—
273	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	16	yes	—
274	C₂×C₄²	—	2	4	no	—
275	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
276	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
277	#95	C₂³×C₁₃₉	1	16	yes	—
278	#95	C₂³×C₁₃₉	1	16	yes	—
279	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
280	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
281	#41	—	2	128	no	—
282	#41	—	2	128	no	—
283	#41	—	2	64	no	—
284	C₂×Q₈	—	2	128	no	—
285	C₂×Q₈	—	2	32	no	—
286	C₂×Q₈	—	2	8	no	—
287	C₂×Q₈	—	2	16	no	—
288	C₂×Q₈	—	2	4	no	—
289	C₂×Q₈	—	2	8	no	—
290	C₂×Q₈	—	2	4	no	—
291	C₂×Q₈	—	2	8	no	—
292	C₂×Q₈	—	2	8	no	—
293	C₂×Q₈	—	2	8	no	—
294	C₂×Q₈	—	2	8	no	—
295	C₂×Q₈	—	4	16	no	—
296	C₂×Q₈	C₂×D₄×C₁₃₉	1	8	yes	—
297	C₂×Q₈	C₂×D₄×C₁₃₉	1	16	yes	—
298	C₂×D₄	—	2	16	no	—
299	C₂×D₄	—	2	8	no	—
300	C₂×D₄	—	2	8	no	—
301	C₂×D₄	—	2	8	no	—
302	C₂×D₄	—	2	4	no	—
303	C₂×D₄	—	2	4	no	—
304	C₂×D₄	C₂×D₄×C₁₃₉	1	16	yes	—
305	C₂×D₄	C₂×D₄×C₁₃₉	1	8	yes	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	16	no	—
308	C₂²×C₄	—	2	8	no	—
309	C₂²×C₄	—	2	16	no	—
310	C₂²×C₄	—	2	16	no	—
311	C₂²×C₄	—	2	8	no	—
312	C₂²×C₄	—	2	8	no	—
313	C₂²×C₄	—	2	8	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	2	8	no	—
316	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
317	C₂²×C₄	C₂×D₄×C₁₃₉	1	16	yes	—
318	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
319	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
320	C₂²×C₄	C₂⁴×C₁₃₉	1	8	yes	—
321	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
322	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
323	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
324	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
325	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
326	C₄⋊C₄	—	2	32	no	—
327	C₄⋊C₄	—	2	8	no	—
328	C₄⋊C₄	—	2	32	no	—
329	C₂²⋊C₄	—	2	8	no	—
330	C₂²⋊C₄	—	2	32	no	—
331	C₂²⋊C₄	—	2	32	no	—
332	C₄²	—	2	8	no	—
333	C₄²	—	2	8	no	—
334	C₂³	—	2	4	no	—
335	C₂³	—	2	4	no	—
336	C₂³	—	2	4	no	—
337	C₂³	—	2	16	no	—
338	C₂³	C₂²×D₄×C₁₃₉	1	8	yes	—
339	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
340	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
341	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
342	Q₈	—	2	32	no	—
343	Q₈	—	2	16	no	—
344	Q₈	—	2	32	no	—
345	Q₈	—	4	16	no	—
346	D₄	—	2	32	no	—
347	D₄	—	2	32	no	—
348	D₄	—	2	16	no	—
349	C₂×C₄	—	2	64	no	—
350	C₂×C₄	—	2	16	no	—
351	C₂×C₄	—	2	16	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	8	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	32	no	—
358	C₂×C₄	—	2	8	no	—
359	C₂×C₄	—	2	8	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	16	no	—
362	C₂×C₄	—	4	8	no	—
363	C₂×C₄	#120×C₁₃₉	1	16	yes	—
364	C₂×C₄	C₂²×D₄×C₁₃₉	1	8	yes	—
365	C₂×C₄	C₂²×D₄×C₁₃₉	1	8	yes	—
366	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
367	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
368	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
369	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	8	yes	complemented
370	C₂²	—	2	4	no	—
371	C₂²	—	2	8	no	—
372	C₂²	—	2	8	no	—
373	C₂²	—	2	16	no	—
374	C₂²	—	4	8	no	—
375	C₂²	—	4	8	no	—
376	C₂²	C₂×#120×C₁₃₉	1	4	yes	—
377	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
378	C₂²	C₂³×D₄×C₁₃₉	1	2	yes	—
379	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	4	yes	—
380	C₄	—	2	8	no	—
381	C₄	—	2	8	no	—
382	C₄	—	2	8	no	—
383	C₄	—	4	4	no	—
384	C₄	—	4	8	no	—
385	C₄	C₂×#120×C₁₃₉	1	8	yes	—
386	C₂	—	2	4	no	—
387	C₂	—	4	8	no	—
388	C₂	C₂²×#120×C₁₃₉	1	1	yes	characteristic
389	C₂	#3486×C₁₃₉	1	2	yes	—
390	C₂	#3499×C₁₃₉	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂²×2₋¹⁺⁴×C₁₃₉	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂×#536×C₁₃₉	C₂	semidirect
3. C₂²×C₄⋊Q₈×C₁₃₉	C₂	semidirect
4. #2434×C₁₃₉	C₂	semidirect
5. #2432×C₁₃₉	C₂	semidirect
6. #2406×C₁₃₉	C₂	semidirect
7. #2310×C₁₃₉	C₂	semidirect
8. #2297×C₁₃₉	C₂	semidirect
173. C₂×C₄×C₁₃₉	2₋¹⁺⁴	semidirect
195. #35666	C₁₃₉	direct (N × H)
196. C₁₃₉	#35666	direct (N × H)
198. C₂×#536	C₂×C₁₃₉	semidirect
199. C₂²×C₄⋊Q₈	C₂×C₁₃₉	semidirect
200. #2434	C₂×C₁₃₉	semidirect
201. #2432	C₂×C₁₃₉	semidirect
202. #2406	C₂×C₁₃₉	semidirect
203. #2310	C₂×C₁₃₉	semidirect
204. #2297	C₂×C₁₃₉	semidirect
369. C₂×C₄	2₋¹⁺⁴×C₁₃₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×2₋¹⁺⁴×C₁₃₉	2
C₂×#536×C₁₃₉	2
C₂²×C₄⋊Q₈×C₁₃₉	2
#2434×C₁₃₉	2
#2432×C₁₃₉	2
#2406×C₁₃₉	2
#2310×C₁₃₉	2
#2297×C₁₃₉	2
#35666	139

Subgroups — C139×#35666 #48030262

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#35666 #48030262